A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm s⁻¹. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap shot of the wave is shown in figure. The velocity of P when its displacement is 5 cm is:

Question

G1 Physics · Accepted Answer

Step 1: ω = 2πv/λ = 2π(0.10)/0.50 = 0.4π s⁻¹. Step 2: Particle speed magnitude at y = 0.05 m is ω√(A²-y²) = 0.4π√(0.10²-0.05²) = √3π/50 m s⁻¹. Step 3: The snapshot fixes the upward direction at P. Final: C.